We present an algorithm to study mixed-state dynamics in one-dimensional quantum lattice systems. The algorithm can be used, e.g., to construct thermal states or to simulate real time evolution given by a generic master equation. Its two main ingredients are (i) a superoperator renormalization scheme to efficiently describe the state of the system and (ii) the time evolving block decimation technique to efficiently update the state during a time evolution. The computational cost of a simulation increases significantly with the amount of correlations between subsystems, but it otherwise depends only linearly on the system size. We present simulations involving quantum spins and fermions in one spatial dimension.

With the continued improvement of sequencing technologies, the prospect of genome-based medicine is now at the forefront of scientific research. To realize this potential, however, a revolutionary sequencing method is needed for the cost-effective and rapid interrogation of individual genomes. This capability is likely to be provided by a physical approach to probing DNA at the single-nucleotide level. This is in sharp contrast to current techniques and instruments that probe ͑through chemical elongation, electrophoresis, and optical detection͒ length differences and terminating bases of strands of DNA. Several physical approaches to DNA detection have the potential to deliver fast and low-cost sequencing. Central to these approaches is the concept of nanochannels or nanopores, which allow for the spatial confinement of DNA molecules. In addition to their possible impact in medicine and biology, the methods offer ideal test beds to study open scientific issues and challenges in the relatively unexplored area at the interface between solids, liquids, and biomolecules at the nanometer length scale. This Colloquium emphasizes the physics behind these methods and ideas, critically describes their advantages and drawbacks, and discusses future research opportunities in the field.

A rapid and low-cost method to sequence DNA would usher in a revolution in medicine. We propose and theoretically show the feasibility of a protocol for sequencing based on the distributions of transverse electrical currents of single-stranded DNA while it translocates through a nanopore. Our estimates, based on the statistics of these distributions, reveal that sequencing of an entire human genome could be done with very high accuracy in a matter of hours without parallelization, e.g., orders of magnitude faster than present techniques. The practical implementation of our approach would represent a substantial advancement in our ability to study, predict and cure diseases from the perspective of the genetic makeup of each individual.Recent innovations in manufacturing processes have made it possible to fabricate devices with pores at the nanometer scale [1][2][3][4][5], i.e., the scale of individual nucleotides. This opens up fascinating new venues for sequencing DNA. For instance, one suggested method is to measure the so called blockade current [6][7][8][9][10][11][12][13][14][15][16][17][18][19]. In this method, a longitudinal electric field is applied to pull DNA through a pore. As the DNA goes through, a significant fraction of ions is blocked from simultaneously entering the pore. By continuously measuring the ionic current, single molecules of DNA can be detected. Other methods using different detection schemes, ranging from optical [20] to capacitive [21], have also been suggested. Despite much effort, however, single nucleotide resolution has not yet been achieved [22].In this Letter, we explore an alternative idea which would allow single-base resolution by measuring the electrical current perpendicular to the DNA backbone while a single strand immersed in a solution translocates through a pore. To do this, we envision embedding electrodes in the walls of a nanopore as schematically shown in the inset of Figure 1. The realization of such a configuration, while difficult to achieve in practice, is within reach of present experimental capabilities [1][2][3][4][5]. The DNA is sequenced by using the measured current as an electronic signature of the bases as they pass through the pore. We couple molecular dynamics simulations and quantum mechanical current calculations to examine the feasibility of this approach. We find that if some control is exerted over the DNA dynamics, the distributions of current values for each nucleotide will be sufficiently different to allow for rapid sequencing. We show that a transverse field of the same magnitude as that driving the current provides sufficient control.We first discuss an idealized case of DNA dynamics which sets the foundations for the approach we describe. Second, we look at the distributions of transverse currents through the nucleotides in a realistic setting using a combination of quantum-mechanical calculations of current and molecular dynamics simulations of DNA translocation through the pore. We use a Green's function method to calculate the c...

We report theoretical studies of charge transport in single-stranded DNA in the direction perpendicular to the backbone axis. We find that, if the electrodes which sandwich the DNA have the appropriate spatial width, each nucleotide carries a unique signature due to the different electronic and chemical structure of the four bases. This signature is independent of the nearest-neighbor nucleotides. Furthermore, except for the nucleotides with Guanine and Cytosine bases, we find that the difference in conductance of the nucleotides is large for most orientations of the bases with respect to the electrodes. By exploiting these differences it may be possible to sequence single-stranded DNA by scanning its length with conducting probes.

Thermodynamic methods based on conductor-like screening models (COSMO) originated from the use of solvation thermodynamics and computational quantum mechanics. These methods rely on sigma profiles specific to each molecule. A sigma profile is the probability distribution of a molecular surface segment having a specific charge density. Two COSMO-based thermodynamic models are COSMO-RS (realistic solvation) developed by Klamt and his colleagues, and COSMO-SAC (segment activity coefficient) published by Lin and Sandler. Quantum mechanical calculations for generating the sigma profiles represent the most time-consuming and computationally expensive aspect of using COSMO-based methods. A growing number of scientists and engineers are interested in the COSMO-based thermodynamic models but are intimidated by the complexity of performing quantum mechanical calculations. This paper presents the first free, web-based sigma profile database of 1432 compounds. We describe the procedure for sigma profile generation, and we have validated our database by comparing COSMO-based predictions of activity coefficients, normal boiling point and solubility with experimental data and thermodynamic property database. We discuss improvements which include using supplemental geometry optimization software packages to provide good initial guesses for molecular conformations as a precursor to the COSMO calculation. Finally, this paper provides a FORTRAN program and a procedure to generate additional sigma profiles, as well as a FORTRAN program to generate binary phase-equilibrium predictions using the COSMO-SAC model. Our sigma profile database will facilitate predictions of thermodynamic properties and phase behaviors from COSMO-based thermodynamic models.

We report first-principles calculations of local heating in nanoscale junctions formed by a single molecule and a gold point contact. Due to the lower current density and larger heat dissipation, the single molecule heats up less than the gold point contact. We also find that, at zero temperature, a threshold bias Vonset of about 6 mV and 11 mV for the molecule and the point contact, respectively, is required to excite the smallest vibrational mode and generate heat. The latter estimate is in very good agreement with recent experimental results on the same system. At a given external bias V below Vonset, heating becomes noticeable when the background temperature is on the order of ∼ e(Vonset − V )/kB. Above Vonset, local heating increases dramatically with increasing bias but is also considerably suppressed by thermal dissipation into the electrodes. The results provide a microscopic picture of current-induced heat generation in atomic-scale structures.

Uncertainty relations provide constraints on how well the outcomes of incompatible measurements can be predicted, and, as well as being fundamental to our understanding of quantum theory, they have practical applications such as for cryptography and witnessing entanglement. Here we shed new light on the entropic form of these relations, showing that they follow from a few simple entropic properties, including the data processing inequality. We prove these relations without relying on the exact expression for the entropy, and hence show that a single technique applies to several entropic quantities, including the von Neumann entropy, min-and max-entropies and the Rényi entropies.

Ion channels play a key role in regulating cell behavior and in electrical signaling. In these settings, polar and charged functional groups – as well as protein response – compensate for dehydration in an ion-dependent way, giving rise to the ion selective transport critical to the operation of cells. Dehydration, though, yields ion-dependent free-energy barriers and thus is predicted to give rise to selectivity by itself. However, these barriers are typically so large that they will suppress the ion currents to undetectable levels. Here, we establish that graphene displays a measurable dehydration-only mechanism for selectivity of K+ over Cl−. This fundamental mechanism – one that depends only on the geometry and hydration – is the starting point for selectivity for all channels and pores. Moreover, while we study selectivity of K+ over Cl−, we find that dehydration-based selectivity functions for all ions, i.e., cation over cation selectivity (e.g., K+ over Na+). Its likely detection in graphene pores resolves conflicting experimental results, as well as presents a new paradigm for characterizing the operation of ion channels and engineering molecular/ionic selectivity in filtration and other applications.